Improved compound poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain Export

@article{citeulike:3090395, abstract = {We derive a new compound Poisson distribution with explicit parameters to approximate the number of overlapping occurrences of any set of words in a Markovian sequence. Using the Chen-Stein method, we provide a bound for the approximation error. This error converges to 0 under the rare event condition, even for overlapping families, which improves previous results. As a consequence, we also propose Poisson approximations for the declumped count and the number of competing renewals. {\copyright} Applied Probability Trust 2007.}, address = {INRA, Unite? Mathe?matique Informatique et Ge?nome, F-78352 Jouy-en-Josas, France}, author = {Roquain, E. and Schbath, S.}, citeulike-article-id = {3090395}, citeulike-linkout-0 = {http://dx.doi.org/10.1239/aap/1175266472}, citeulike-linkout-1 = {http://www.scopus.com/record/display.url?view=extended&origin=resultslist&eid=2-s2.0-34247618196}, doi = {10.1239/aap/1175266472}, journal = {Advances in Applied Probability}, keywords = {rarewords}, number = {1}, pages = {128--140}, posted-at = {2008-08-06 11:14:05}, priority = {2}, title = {Improved compound poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain}, url = {http://dx.doi.org/10.1239/aap/1175266472}, volume = {39}, year = {2007} }

TY - JOUR ID - citeulike:3090395 L3 - citeulike-article-id:3090395 N2 - We derive a new compound Poisson distribution with explicit parameters to approximate the number of overlapping occurrences of any set of words in a Markovian sequence. Using the Chen-Stein method, we provide a bound for the approximation error. This error converges to 0 under the rare event condition, even for overlapping families, which improves previous results. As a consequence, we also propose Poisson approximations for the declumped count and the number of competing renewals. © Applied Probability Trust 2007. IS - 1 JF - Advances in Applied Probability AD - INRA, Unite? Mathe?matique Informatique et Ge?nome, F-78352 Jouy-en-Josas, France EP - 140 TI - Improved compound poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain VL - 39 SP - 128 KW - rarewords AU - Roquain, E AU - Schbath, S PY - 2007/// UR - http://dx.doi.org/10.1239/aap/1175266472 ER -